Evolution of Robustness to Noise and Mutation in Gene Expression Dynamics

Phenotype of biological systems needs to be robust against mutation in order to sustain themselves between generations. On the other hand, phenotype of an individual also needs to be robust against fluctuations of both internal and external origins that are encountered during growth and development. Is there a relationship between these two types of robustness, one during a single generation and the other during evolution? Could stochasticity in gene expression have any relevance to the evolution of these robustness? Robustness can be defined by the sharpness of the distribution of phenotype; the variance of phenotype distribution due to genetic variation gives a measure of `genetic robustness' while that of isogenic individuals gives a measure of `developmental robustness'. Through simulations of a simple stochastic gene expression network that undergoes mutation and selection, we show that in order for the network to acquire both types of robustness, the phenotypic variance induced by mutations must be smaller than that observed in an isogenic population. As the latter originates from noise in gene expression, this signifies that the genetic robustness evolves only when the noise strength in gene expression is larger than some threshold. In such a case, the two variances decrease throughout the evolutionary time course, indicating increase in robustness. The results reveal how noise that cells encounter during growth and development shapes networks' robustness to stochasticity in gene expression, which in turn shapes networks' robustness to mutation. The condition for evolution of robustness as well as relationship between genetic and developmental robustness is derived through the variance of phenotypic fluctuations, which are measurable experimentally.Comment: 25 page

Shaping Robust System through Evolution

Biological functions are generated as a result of developmental dynamics that form phenotypes governed by genotypes. The dynamical system for development is shaped through genetic evolution following natural selection based on the fitness of the phenotype. Here we study how this dynamical system is robust to noise during development and to genetic change by mutation. We adopt a simplified transcription regulation network model to govern gene expression, which gives a fitness function. Through simulations of the network that undergoes mutation and selection, we show that a certain level of noise in gene expression is required for the network to acquire both types of robustness. The results reveal how the noise that cells encounter during development shapes any network's robustness, not only to noise but also to mutations. We also establish a relationship between developmental and mutational robustness through phenotypic variances caused by genetic variation and epigenetic noise. A universal relationship between the two variances is derived, akin to the fluctuation-dissipation relationship known in physics

Starling flock networks manage uncertainty in consensus at low cost

Flocks of starlings exhibit a remarkable ability to maintain cohesion as a group in highly uncertain environments and with limited, noisy information. Recent work demonstrated that individual starlings within large flocks respond to a fixed number of nearest neighbors, but until now it was not understood why this number is seven. We analyze robustness to uncertainty of consensus in empirical data from multiple starling flocks and show that the flock interaction networks with six or seven neighbors optimize the trade-off between group cohesion and individual effort. We can distinguish these numbers of neighbors from fewer or greater numbers using our systems-theoretic approach to measuring robustness of interaction networks as a function of the network structure, i.e., who is sensing whom. The metric quantifies the disagreement within the network due to disturbances and noise during consensus behavior and can be evaluated over a parameterized family of hypothesized sensing strategies (here the parameter is number of neighbors). We use this approach to further show that for the range of flocks studied the optimal number of neighbors does not depend on the number of birds within a flock; rather, it depends on the shape, notably the thickness, of the flock. The results suggest that robustness to uncertainty may have been a factor in the evolution of flocking for starlings. More generally, our results elucidate the role of the interaction network on uncertainty management in collective behavior, and motivate the application of our approach to other biological networks.Comment: 19 pages, 3 figures, 9 supporting figure

Predicting Phenotypic Diversity and the Underlying Quantitative Molecular Transitions

During development, signaling networks control the formation of multicellular patterns. To what extent quantitative fluctuations in these complex networks may affect multicellular phenotype remains unclear. Here, we describe a computational approach to predict and analyze the phenotypic diversity that is accessible to a developmental signaling network. Applying this framework to vulval development in C. elegans, we demonstrate that quantitative changes in the regulatory network can render ~500 multicellular phenotypes. This phenotypic capacity is an order-of-magnitude below the theoretical upper limit for this system but yet is large enough to demonstrate that the system is not restricted to a select few outcomes. Using metrics to gauge the robustness of these phenotypes to parameter perturbations, we identify a select subset of novel phenotypes that are the most promising for experimental validation. In addition, our model calculations provide a layout of these phenotypes in network parameter space. Analyzing this landscape of multicellular phenotypes yielded two significant insights. First, we show that experimentally well-established mutant phenotypes may be rendered using non-canonical network perturbations. Second, we show that the predicted multicellular patterns include not only those observed in C. elegans, but also those occurring exclusively in other species of the Caenorhabditis genus. This result demonstrates that quantitative diversification of a common regulatory network is indeed demonstrably sufficient to generate the phenotypic differences observed across three major species within the Caenorhabditis genus. Using our computational framework, we systematically identify the quantitative changes that may have occurred in the regulatory network during the evolution of these species. Our model predictions show that significant phenotypic diversity may be sampled through quantitative variations in the regulatory network without overhauling the core network architecture. Furthermore, by comparing the predicted landscape of phenotypes to multicellular patterns that have been experimentally observed across multiple species, we systematically trace the quantitative regulatory changes that may have occurred during the evolution of the Caenorhabditis genus

Analysis of feedback loops and robustness in network evolution based on Boolean models

<p>Abstract</p> <p>Background</p> <p>Many biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention.</p> <p>Results</p> <p>In this paper, we focus on the robustness of a network that is acquired during its evolutionary process. Through simulations using Boolean network models, we found that preferential attachment increases the number of coupled feedback loops in the course of network evolution. Whereas, if networks evolve to have more coupled feedback loops rather than following preferential attachment, the resulting networks are more robust than those obtained through preferential attachment, although both of them have similar degree distributions.</p> <p>Conclusion</p> <p>The presented analysis demonstrates that coupled feedback loops may play an important role in network evolution to acquire robustness. The result also provides a hint as to why various biological networks have evolved to contain a number of coupled feedback loops.</p

Robustness in the long run: Auto-teaching vs Anticipation in Evolutionary Robotics

In Evolutionary Robotics, auto-teaching networks, neural networks that modify their own weights during the life-time of the robot, have been shown to be powerful architectures to develop adaptive controllers. Unfortunately, when run for a longer period of time than that used during evolution, the long-term behavior of such networks can become unpredictable. This paper gives an example of such dangerous behavior, and proposes an alternative solution based on anticipation: as in auto-teaching networks, a secondary network is evolved, but its outputs try to predict the next state of the robot sensors. The weights of the action network are adjusted using some back-propagation procedure based on the errors made by the anticipatory network. First results -- in simulated environments -- show a tremendous increase in robustness of the long-term behavior of the controller

The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks

We investigate how scale-free (SF) and Erdos-Renyi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we find that networks with SFin topologies, that is SF topology for incoming nodes and ER topology for outgoing nodes, are significantly more evolvable towards specific oscillatory targets than networks with ER topology for both incoming and outgoing nodes. Similar results are found for networks with SFboth and SFout topologies. The functionality of the SFout topology, which most closely resembles the structure of biological gene networks (Babu et al., 2004), is compared to the ER topology in further detail through an extension to multiple target outputs, with either an oscillatory or a non-oscillatory nature. For multiple oscillatory targets of the same length, the differences between SFout and ER networks are enhanced, but for non-oscillatory targets both types of networks show fairly similar evolvability. We find that SF networks generate oscillations much more easily than ER networks do, and this may explain why SF networks are more evolvable than ER networks are for oscillatory phenotypes. In spite of their greater evolvability, we find that networks with SFout topologies are also more robust to mutations than ER networks. Furthermore, the SFout topologies are more robust to changes in initial conditions (environmental robustness). For both topologies, we find that once a population of networks has reached the target state, further neutral evolution can lead to an increase in both the mutational robustness and the environmental robustness to changes in initial conditions.Comment: 16 pages, 15 figure